2003 Mustang V6 - Car Tries To Start Itself

Hello, Hoping someone could help me out. It's been less than one month since I purchased a used 2003 Musting from a Ford. The car had 37,000 miles on it. Have had no problems with it until yesterday. When I parked the car, tried to shut it off, took the key out of the ignition, the car persisted to start itself. I not only tried once but it happened about 9 consecutive times and when I drive it over to Ford's maintenance dept, the problem disappears (ugh!!!). You know when your battery is dead and you continue to true to start the car and it makes that sound like its really trying to start but it can't make it? That's the sound. I was of course, very surprised as I've never seen or had any bad experience with cars. I'm wondering if anyone out there would have heard or seen something like this happen. Ford says they've done diagnostics to see what could be causing this problem but they've not experienced the problem themselves therefore can't make a determination as to what the problem could possibly be. Please Help!

Thank you....